The flow and the transport of particles in the human respiratory system dictate the effectiveness of therapeutic aerosols used in inhaled drug delivery. The aerosol particles are generally inhaled through the mouth, passing by the throat before reaching the targeted areas in the lungs. Therefore, knowledge of the particle deposition in the mouth-throat region is critical in the design of effective inhalation devices for optimum delivery to the lungs. Numerical simulations offer a non-invasive and cost-effective alternative to in vivo and in vitro tests. However, accurate prediction remains a challenge for numerical models due to the complexity of the flow in the extrathoracic airways. A robust immersed boundary method for flow in complex geometries is proposed. This greatly simplifies the task of grid generation and eliminates the problems associated with grid quality that exist for boundary-fitted grid techniques. The proposed method is an extension to the momentum forcing approach onto curvilinear coordinates and applies an iterative procedure to compute the forcing term implicitly, which stabilizes the scheme for higher Reynolds numbers. The use of a curvilinear grid minimizes the number of unused cells outside the geometry and increases the efficiency of the numerical scheme. The method is validated against numerical and experimental data in the literature for a number of test cases on both Cartesian and curvilinear grids. The results show good agreement with previous studies. Direct numerical simulations were performed in a number of realistic mouth and throat geometries obtained from MRI scans. A Lagrangian particle tracking scheme was employed to advance the particles dynamically, and total and regional deposition efficiencies were determined and compared to in vitro data. The effect of inflow turbulence and intersubject variation on deposition was studied. Geometric variation has a large impact on total deposition whereas the effect of inflow turbulence is confined to oral deposition.